Union Debt Management

Transcription

1 Unon Debt Management Juan Equza-Goñ Elsa Faragla Rgas Okonomou October 25 Abstract We study the role of government debt maturty n a monetary unon, n the absence of fscal transfers across countres. Our key fndng s that fscal hedgng s only possble when spendng represents an aggregate shock n the unon. In the case of dosyncratc dsturbances n government spendng, t s not possble to target a portfolo whch provdes fscal nsurance to the governments, the allocaton s one of ncomplete fnancal markets. These mplcatons are n lne wth the emprcal data patterns. Usng a sample of 5 Euro area countres and hstorcal holdng perod returns on government bonds of varous maturtes, we fnd that fscal nsurance s not sgnfcant aganst country specfc shocks, t s sgnfcant aganst aggregate shocks. Our analyss extends the theoretcal results of the lterature on optmal fscal polcy wthout state contngent debt to a two country model. We show that n the two country setup and under an ncomplete market, the optmal tax schedule, consumpton and lesure follow pure a random walk. Keywords: Debt Management, Fscal Polcy, Government Debt, Maturty Structure, Tax Smoothng JEL Classfcaton : E43, E62, H63 Faragla and Okonomou thank the Keynes Fund- Cambrdge for fnancal support. We are greatful to Mrko Abbrtt, Vncent Bodart, Hafedh Bouakez, Chryss Gantsarou, Robert Kollman, Jochen Mankart, Antono Moreno and Romanos Prfts for useful comments and suggestons. We are also greatful to partcpants at the Macroeconomcs Workshop n Blbao. All errors are our own. Unversty of Navarra Unversty of Cambrdge and CEPR. Unversté Catholque de Louvan. IRES-CORE, Unversté Catholque de Louvan, Collège L. H. Duprez, 3 Place Montesqueu 348 Louvan la Neuve, Belgum. Emal: Rgas.Okonomou@uclouvan.be

2 Introducton The recent (and ongong) debt crss n the Euro Area has brought to surface several concerns over the management of government debt labltes. Of partcular nterest n the debate s the noton that governments, through an actve management of the maturty structure, can ensure the solvency of ther nter-temporal budgets, allevate the burden from dstortonary taxaton and refnance ther outstandng labltes when nterest costs are rsng wthout the need to make drastc cuts n spendng or fscal defcts. A szable lterature has shown, n closed economy models, that governments can beneft from ssung long term debt eg. Angeletos (22) Buera and Ncoln (26) (hereafter ABN) and more recently Lustg Sleet and Yeltekn (28). These papers dentfy n long term bonds a hedgng value, the prce of these bonds tends to decrease when adverse spendng shocks ht the economy. Hence, when a government s runnng a large defct, and therefore needs to commt to future surpluses, the need to rase revenue from taxes becomes less urgent, f t can beneft from the nsurance channel offered by long term debt. However, snce these models consder debt management n a closed economy settng, t remans unexplored whether the fscal nsurance channel s avalable n a monetary unon where nomnal and real nterest rates are subject to the strct no arbtrage condtons mposed by nternatonal captal flows. We may thnk, for nstance, that countres whch form a unon beneft f these flows lower the costs of fnancng: when the Spansh government needs to borrow, they face lower costs when the lendng comes from Germany, provded that spendng n Germany has not ncreased and so on. On the other hand, when a government s unable to borrow nternatonally (as n the closed economy models of ABN), an ncrease n spendng pushes up nterest rates; as the analyss of ABN shows, the rse n nterest rates unleashes fscal nsurance. In ths paper we seek to nvestgate whether debt management can serve, n a monetary unon, the role that the closed economy lterature has assgned to t. We model a unon whch conssts of two countres, each has ts own government and prvate sector, and we further assume that debt management and fscal polces are chosen by a benevolent planner under full commtment. Our setup s broadly smlar to ABN, however, when the Ramsey planner solves the optmal polcy problem she now must take nto account the no arbtrage condtons determned by the flow of funds across countres. As we show, these addtonal constrants may nfluence the potental of long bonds to provde fscal nsurance. Our analyss dstngushes between dosyncratc (country specfc) shocks and aggregate (common) shocks n the unon. Under dosyncratc shocks, the rse n the spendng level of one country s completely offset by a drop n the level of spendng n the other country, n the case of aggregate shocks the shft n spendng happens smultaneously n both countres. We then ask: How wll the planner set taxes and the debt portfolo when shocks are dosyncratc and when they are common? Our fndngs are as follows: Frst, we show that n the case of common shocks, debt management serves t usual purpose: It becomes optmal for the planner to choose a portfolo of long term debt and short term savngs. Through ths portfolo governments can take advantage of the debt devaluaton channel studed n ABN. Second, we fnd that when shocks are purely dosyncratc, then debt management cannot provde any nsurance aganst spendng ncreases. In ths case, whether governments ssue long term debt or short term bonds becomes rrelevant. 2

3 To understand these fndngs note that n equlbrum government debt needs to be prced by the households whch hold t. If long bonds provde fscal nsurance to a government then the households whch hold them antcpate to experence a captal loss when spendng levels rse; ths debt devaluaton channel explans why governments want to ssue long bonds n the closed economy. However, n the monetary unon where funds can flow readly across borders, and f shocks are dosyncratc, bonds whch otherwse provde nsurance to the government automatcally qualfy as a good hedge aganst spendng shocks for the households of another country. For ths reason, the bonds are prced by foregn households, and snce prces n equlbrum are proportonal to the expected margnal utlty growth of the bond holder, they now do not provde any nsurance to the government that ssues them. In the compettve equlbrum the planner must set taxes so that margnal utlty growth s equated across countres. Under dosyncratc shocks ths means that the holdng perod returns of long debt cannot be at all responsve to the shocks, n partcular because n one country spendng has ncreased and n the other t has fallen yet the resale prce of these bonds must be equal across countres. In the case where shocks are aggregate, the equalty of the margnal utlty growth rates s not restrctve; as we show, the planner solves a problem whch s very smlar to the closed economy. Our model brngs together debt management and fscal polcy under one authorty, and therefore, t provdes a useful benchmark to analyse how governments should set taxes n the monetary unon when they can fnance defcts wth a portfolo of dfferent debt maturtes. As n ABN, taxes are dstortonary n our model, and the mportance of managng the maturty structure evolves around the goal to smooth tax dstortons over tme. ABN show that when governments can ssue long bonds they can complete the market, the optmal tax schedule s only nfluenced by the (current) level of spendng. Elsewhere, n models whch constran the government not to ssue long bonds, markets are ncomplete (e.g. Ayagar Marcet Sargent and Seppala (22-hereafter AMSS)); n these models taxes feature also a random walk component, summarzed n the Lagrange multplers of the government budget constrant. However, n both cases n the closed economy, taxes are frontloaded, snce t s optmal to ncrease them n perods when lesure drops and when spendng levels are hgh (see e.g. Scott (28)). In our two country model, the planner s objectve s not merely to smooth taxes over tme, but also to smooth tax and consumpton devatons across countres. When we assume that shocks are dosyncratc ths addtonal objectve yelds a very sharp predcton regardng the optmal path of endogenous varables: they should follow a pure random walk process. Snce the optmal polcy must set the growth rates of consumpton equal across countres, the result that taxes should track closely spendng levels, cannot hold. If they dd, then consumpton growth would be postve n the hgh spendng economy, and negatve n the low spendng one. But such an allocaton would volate the equlbrum n the bonds market, that nterest rates and consumpton growth rates are equal across countres. Ths result should be of separate nterest vz the ongong szable tax adjustments n the European contnent. Though n our analyss we treat separately (and for clarty) common and dosyncratc shocks n realty these are two components of the spendng process of each country n the unon. To revst the prevous example, suppose that a large ncrease n expendture occurs n Span, yet spendng levels n Germany reman constant. The shft n expendture clearly has an aggregate 3

4 component and an dosyncratc one (the latter defned as the country devaton from the average). The frst component can be easly nsured aganst through debt management and requres that taxes temporarly ncrease n both countres, the second cannot be nsured and leads to a permanent ncrease n taxes n Span and a decrease n Germany. In secton 5 of our paper we turn to the emprcal evdence to test the relevance of our fndngs. In partcular, we wsh to test the hypothess that dosyncratc shocks cannot be nsured aganst n a monetary unon but that the debt devaluaton channel s potent n response to common shocks. For ths reason, we make use of a unque data set whch ncludes all of the bonds ssued by 5 European countres: Germany, Span, France, Belgum and Italy, as well as hstorcal nformaton on the yeld curves faced by each country. Though our sample does not cover every euro area (EA) country t does account for the bulk of spendng and the bulk of GDP n the EA. We then run panel S-VARs and n the lst of varables we nclude the holdng perod returns and the government spendng shocks. Under fscal nsurance, t must be that the holdng returns deprecate when postve spendng shocks occur. The emprcal analyss provdes strong support n favor of our theoretcal results. We fnd that durng the calm Euro years, between 999 and 27 (2nd quarter) there s very lttle evdence of fscal hedgng aganst dosyncratc shocks (defned as the devaton of country spendng from average spendng), however, there s strong evdence n favor of the hedgng channel of debt management when we look at aggregate shocks. Ths pattern holds for the overall debt portfolo of the countres n our sample, but also separately by maturty. Another contrbuton of our paper s therefore to document carefully the fscal nsurance channel of polcy for a subset of the EA countres. Brendt Sleet and Yeltekn (22) have recently performed a smlar exercse lookng at aggregate US data. Ths paper s related to several strands n the lterature. Frst, there s a long stream of papers analyzng optmal fscal and monetary polces n a monetary unon. Promnent examples nclude Beetsma and Jensen (25), Gal and Monacell (28) and Ferrero (26) and Forlatt (29) among others. Closer to our paper s Ferrero (26). He also consders the Ramsey program under full commtment, however, assumes that only one perod debt s avalable to governments, and hghlghts that taxes contan a random walk component as n AMSS. The key dfference, s that we focus on the debt management, no other paper n the lterature looks at the maturty structure of debt nvestgatng the fscal hedgng propertes of long bonds. Moreover, snce n order to analyse a polcy channel whch s ntmately related to the asset prces, requres us to solve a large scale model usng global methods, our setup s much smpler than the setup of Ferrerro (26). We consder an endowment economy as ABN do and abstract from nflaton; ours s a real model. Papers whch consder monetary polcy explctly add an mportant layer of fscal nsurance: nflaton. In the case where spendng ncreases n one country, an ncrease n the prce level reduces the real payout of government debt. Ths channel has been emphaszed for example n closed economy models by Char and Kehoe (999), SGU (24), Su (24) Lustg et al (28) and FMOS (23) and n the open economy by Ferrerro (26). A noteworthy concluson from ths research s that n models n whch the Phllps curve s calbrated to match the data, the cost of usng nflaton to erode publc debt s very large, the Ramsey planner ends up usng fscal surpluses to fnance spendng shocks. In the monetary unon ths nflaton channel s subject to further restrctons stemmng from the fact that monetary polcy s common across the member states. For these reasons we have left 4

5 nflaton outsde of our model, ths can be vewed as an extreme scenaro whereby monetary polcy s devoted to stablzng the prce level. In the emprcal secton, however, we do allow for nflaton to exert an nfluence; our emprcal estmates contnue to refute that government bond prces respond to dosyncratc dsturbances. A consderable lterature has emphaszed the dstncton between dosyncratc and aggregate shocks as a very mportant aspect of the decson of countres to form (or jon) a currency unon (e.g. Mundell (96), Frankel and Rose (998), and Fahr and Wernng (24) more recently). The key nsght from ths lterature, s that when shocks are strongly correlated across countres jonng a currency area and delegatng monetary polcy may be optmal, however, when busness cycles are not correlated then the common polcy wll aggravate economc fluctuatons. Though our setup s based solely on government spendng shocks, these shocks are a major source of economc fluctuatons n standard macroeconomc models. Moreover, n contrast to the rest of the lterature whch studes the tradeoff stemmng from common monetary polcy, our arguments are based on debt management, however, the concluson we obtan from our model s smlar. Wthn the same ven, a recent stream of papers nvestgates the role played by fscal transfers n fscal unons. Fahr and Wernng (24) consder the mportance prce and wage rgdtes n determnng the benefts from transfers, under complete and ncomplete markets. Dmtrev and Hoddenbagh (25) study fscal polces under mperfect rsk-sharng and n the presence of terms of trade externaltes to dentfy condtons under whch fscal unons are optmal. Both papers emphasze the role of assymetres n economc shocks. Though not the man focus of our study, we characterze the debt management polces and tradeoffs n a world where fscal transfers are allowed across countres. We show that transfers enable governments to complete the market through ther common debt ssuances. Our conclusons are therefore relevant for ths strand of the lterature. Ths paper proceeds as follows: Secton 2 presents the model. Secton 3 derves the optmalty condtons from the Ramsey program and presents analytcal results on the optmal debt management strategy. Secton 4 solves the model numercally to characterze the optmal tax polcy. Secton 5 presents the emprcal evdence. A fnal secton concludes. 2 The Model 2. Preferences, Uncertanty and Fnancal Markets. 2.. Preferences Our model s n three perods t =,, 2 and descrbes the Ramsey equlbrum wth full commtment. 2 We assume that there are two countres, each populated by a household and a government. Household preferences are represented by E u(c, l ) + βu(c, l ) + β 2 u(c 2, l 2) where =, 2 denotes the country and E s the expectaton operator condtonal on the perod nformaton set. c t and l t denote consumpton and lesure respectvely. We assume that u x >, u xx < for x = c, l and u c,l =. β denotes the dscount factor. See Frankel and Rose (998) for a model whch endogenzes ths tradeoff. 2 See also Nosbusch (28) for a 3 perod model of optmal government debt management n the closed economy. 5

6 2..2 Technology Followng ABN, AMSS and Faragla, Marcet, Okonomou and Scott (25 (a)- hereafter FMOS) we assume that output s produced through a lnear technology wth labor as the sole nput. Households are endowed wth a unt of tme every perod. We can wrte: yt = ( lt) where yt s output n country n t Uncertanty We assume that government spendng shocks ht the economy only n perod t =. In other perods government spendng (n both countres) s constant, equal to a steady state level g. Formally, we have: g t = g for t =, 2 and =, 2 and g s a random varable wth g {g L, g H }, g H > g L and (g H +g L ) 2 = g. We further assume that P rob(g = g L ) = P rob(g = g H ) = 2. Of partcular mportance for our analyss s the correlaton of the shocks between countres. We wll concentrate on two polar cases: ) g and g 2 are perfectly negatvely correlated.e. P rob(g = g L g = g H ) = 2 and ) g and g 2 are perfectly postvely correlated, e.g. P rob(g = g L g = g H ) =. We restrct our analyss to ) and ) for the followng reasons: Frst, snce we consder a model n three perods, the longest maturty we can ntroduce s a two perod bond. If governments have access to one perod and two perod debt at t =, then n prncple, they can reproduce the complete market outcome of ABN, f there are two states of spendng and the returns of the bonds are not perfectly collnear. Second, as dscussed prevously we wsh to study separately the case where government spendng represents a pure dosyncratc dsturbance and the case where t represents an aggregate shock to the unon. Under ) we have g = 2g, so that shocks are purely dosyncratc, overall spendng remans constant n the monetary unon n t =,, 2. Under ) we have g {2g L, 2g H } and therefore shocks are aggregate Government Taxaton and Debt To fnance spendng, governments n both countres ssue debt and levy dstortonary taxes on labor ncome. We assume that government debt can be ssued (n perod ) n two maturtes, a short term bond (maturty of one year) and a long bond of two year maturty. In t = t s only possble to ssue debt n one year maturty. 4 Let us denote by b, b the short and long bonds ssued at t = and b the short term debt ssued n perod t =. denotes the country whose government ssues the debt. We can wrte the government budget constrants n as follows: b + b = b + g τ ( l ) () b = b R + b R, + g τ ( l ) = b R + g τ 2( l 2) for =, 2. R t denotes the return of short term bonds ssued by government and R s the holdng 3 Clearly, any spendng process can be decomposed nto orthogonal aggregate and dosyncratc shocks. Our analyss can be easly extended to more general processes. 4 Snce we assume that there are no shocks after t =, one bond can complete the market. 6

7 perod return of long bonds (buyng long debt n perod and sell n t = as short debt). b denotes an ntal lablty of the government, the outstandng debt level at t = Household Optmzaton We assume that households take government polces as gven. They choose n every perod consumpton, lesure and a portfolo of bonds (domestc and foregn, short and long) to maxmze utlty. Denote by (b,j, b,j and b,j), the holdngs of bonds ssued by government by the country j household. We wll assume that households can take any poston n the bond market, ncludng to ssue debt themselves. Ths assumpton brngs two features to our model: frst, governments can save n any maturty, t s possble for the overall debt ssued by a government to become negatve. Second, households can wrte debt contracts, n equlbrum the net poston of the prvate sector must balance wth the total debt ssued by governments. Practcally, the model allows for prvate debt, however, prvate bonds do not need to be modelled explctly, snce we allow the postons n the government bond market to take any value. The budget constrants of the households are gven by: b,j + b,j = b,j + ( τ)( j l) j c j, (2) b,j = b,jr + b,j R + ( τ)( j l) j c j j = b,jr + ( τ j 2)( l j 2) c j 2 for =, 2 and j =, 2. The frst equaton n (2) gves the constrant n t =. b,j + b,j s the portfolo chosen by the household n that perod. The term b,j represents the savngs of household j n government bonds ssued by country before perod. Snce, as dscussed prevously, we do not focus on these ntal condtons, we wll assume b,j = for j and b, = b. In words, all of the ntal government debt s held domestcally. Ths assumpton s nnocuous for our results. Households maxmze utlty subject to the constrant set (2). In the appendx we characterze the frst order condtons from ths program. We establsh that the followng condtons hold: (3) (4) R = u c(c j ) βe u c (c j ), R = u c(c j ) βu c (c j 2), R = u c(c j 2) u c (c j ) u c (c j ) βe u c (c j 2) ( τt ) = u l(lt) u c (c t) for =, 2 and j =, 2. (4) gves the standard equalty between the margnal rate of substtuton of consumpton and lesure and the net wage receved by the household. (3) gves the Euler equatons whch equate the cost from an extra unt of savngs n a partcular maturty to the future dscounted beneft. Notce that R = uc(cj ) s an expresson whch does not nvolve any uncertanty. Clearly, βu c(c j 2 ) 5 Wthout loss of generalty we can normalze R = = R =. Our am s to dscuss the optmal portfolo choce through a date Ramsey program. In other words, we wll not constran the planner to any consumpton commtment nfluenced by ntal condtons ths follows FMOS (25 b). Such commtments are of lttle relevance for the forces we wsh to hghlght. 7

8 snce we have assumed that all shocks are revealed after perod, the return on debt ssued n t = s not random. Fnally, the term uc(cj 2 ) u c(c j u c(c j ) represents the return on two perod bonds, bought n t =, then ) βe u c(c j 2 ) sold as one perod debt n t =. The prce of two perod debt at t = s β2 E u c(c j 2 ) ; the prce of one u c(c j ) perod debt n t = s βuc(cj 2 ). The holdng perod return R u c(c j ) s the rato of the latter over the former. 2.2 Equlbrum Defnton. The compettve equlbrum s a collecton of prces (R, R R ), quanttes (c t, l t, b t,j, b,j), (b t, b and taxes (τ t ) such that ) households maxmze utlty subject to the constrant set (2) (e.g. the returns satsfy (3) and taxes satsfy (4)). ) government debt and taxes satsfy the budget constrants (). ) the resource constrant of the economy holds (.e. =,2 [c t + gt + lt ] = ). v) Bond markets clear: (5) b,j = b j=,2 b,j = b j=,2 b,j = b statng that the total supply of bonds of any maturty and any perod, equals the total net demand of debt by the households. j=, No Arbtrage In the planner s program (next subsecton) we wll mpose that the optmal allocaton needs to satsfy equatons (3) and (4). Snce under (3) we have that the return Rt s equated to the margnal utlty rato n both countres we have that R = uc(c ) = uc(c2 βe u c(c ) ) βe u c(c 2). Smlarly, R = uc(c ) = uc(c2 βu c(c ) and 2 ) βu c(c 2 2 ) u also c(c ) = uc(c2 β 2 E u c(c ) 2 ) β 2 E u c(c for the two perod maturty. 2 2 ) These condtons derve from the assumpton that government debt s traded n one market, where households can purchase bonds anonymously facng a common prce. If they faled to hold, then the demands for government debt would dverge to ether plus or mnus nfnty. 6 arbtrage) constrants wll be mposed to the optmal program. These addtonal (no 2.3 Ramsey Program Our formulaton of the planner s program s standard and follows closely ABN and AMSS. The planner chooses a sequences of taxes and debt to maxmze E =,2 t=,,2 βt u(c t, lt) subject to 7 the government and household budget constrants, and condtons (3) and (4). To smplfy we make use of the government and household constrants n country (subtractng one from the other) 6 u For example, f we have that c(c ) β 2 E u c(c 2 ) > uc(c2 ) β 2 E u c(c then gven the prce of two year bonds, ether household 2 2 ) sets b, = or household 2 sets b, = + or both. Market clearng (5) does not hold n ether case. 7 We assume that the countres are of equal sze and assgn an equal weght to the households. Many papers have consdered optmal polcy wth unequal country szes, ths s clearly mportant to analyze the mpact of asymmetres on welfare outcomes under a common polcy (for example monetary polcy). Here, we allow tax polces to be country specfc, therefore our results do not hnge crucally on the relatve country szes. In secton 4 we wll consder the case where a fscal shock orgnatng n one country, has an aggregate and an dosyncratc component, ths can be vewed as the case where the larger country experences a shock to spendng. Our results on debt management reman, we show that the dosyncratc component s unnsurable. 8

9 to derve the followng expressons for the constrants n perod : (6) b + b b j, j bj, = b j b j, +g ( l ) + c, =, 2 } {{ } = 8 These expressons can be further rearranged nto: (7) (8) b,2 b 2, + b,2 b 2, = g ( l) + c [c + g ( l)] = =,2 Equaton (7) governs the net flows of funds across the two countres n t =. It states that the consumpton and spendng n country can be fnanced through domestc ncome and through foregn loans. Equaton (8) s the (unon-wde) resource constrant. Smlarly, for perods and 2 we can wrte: (9) () b,2 b 2, = (b,2 b 2 u c (c ),) βe u c (c ) + ( b,2 b 2,) u c(c 2) u c (c ) u c (c ) βe u c (c 2) + g ( l) + c = (b,2 b 2,) u c(c ) βu c (c 2) + g ( l 2) + c 2 and the resource constrants n t =, 2 omtted for brevty. Note that n (9) and () we have mposed the equalty of the margnal utlty ratos across countres; we therefore derve the returns only n terms of c t. The Ramsey program can be represented through the followng Lagrangan: Program β =,2 β 2 =,2 L = E { λ 2 λ t=,,2 =,2 β t u(c t, lt) =,2 λ [ ] b,j + b,j b + s(c, l) j=,2 [ ( ) ] b,j b u (c ),j βe j=,2 u (c ) b u (c 2) u (c ),j + s(c u (c ) βe u (c, l) 2) [ ] b u (c ),j βu (c 2) + s(c 2, l2) ( β t ξ t c t + gt ( lt) ) j=,2 t=,,2 φ [(b,2 b 2,) + ( b,2 b 2,) c g + l [ ] φ β b,2 b 2, (b,2 b 2 u (c ),) βe u (c ) ( b,2 b 2,) u (c 2) u (c ) u (c ) βe u (c 2) c g + l [ ]} φ 2 β 2 (b,2 b 2,) u (c ) βu (c 2) c 2 g2 + l2 ( u (c )E u (c 2 t ) u (c 2 )E u (c t ) ) ( E κ u (c )u (c 2 2) u (c 2 )u (c 2) ) t=,2 κ t where the λs, φs, ξs and κs represent multplers on the constrants. 8 Snce we have assumed that all ntal debt s domestcally held we have that j bj, = b, = b. Hence, on the RHS of (6) ntal debt drops out. ] 9

10 2.3. Complete and Incomplete Markets Program wll be used to solve for the optmal allocaton under both dosyncratc and aggregate shocks. As dscussed prevously, n the former case, the allocaton wll be one of ncomplete markets and n the latter t wll correspond to the complete market allocaton. As s well known, when markets are complete, the planner has at her dsposal state contngent debt. Though we dd not model explctly ths program, followng the arguments n ABN, Program may yeld the complete market outcome f the planner can explot varatons n bond returns so that the propertes of the portfolo, resemble the propertes of state contngent debt. In contrast, when the returns Rt and R t do not vary across states, then we wll have an equlbrum wthout state contngent debt as n AMSS. In the followng paragaphs we progressvely dscuss several features of the complete and ncomplete market allocatons whch are partcularly mportant for our results Optmalty We offer a complete characterzaton of the frst order condtons from Program n the onlne appendx. In ths paragraph we consder a subset of these condtons whch are useful to hghlght the propertes of taxes n the model; we concentrate on the process of the multplers λ t, φ t and the frst order condtons for c t, t =,, 2. These can be wrtten as follows: [ u c (c ) λ s c (c, l) ξ λ u c (c ) u cc(c )s(c, l) + I = φ + [ (g ( l) + c ) ] ] u cc (c ) u c (c + u cc(c () ) u c (c ) λ b κ t u cc (c )E u (c t )I = + κ t u cc (c )E u (c t )I =2 = }{{} t=,2 t=,2 Ψ β [ [ u c (c, l) ξ λ s c (c, l) λ u c (c ) u cc(c )s(c, l) + I = φ + u ]] cc(c ) u c (c ) (g + c + l ) +I = [ t=,2 κ t ( u (c )u cc (c t) ) κ ( ucc (c )u (c 2 2) )] I =2 [ t=,2 κ t ( u (c )u cc (c t) ) κ ( ucc (c )u (c 2 2) )] [ ] λ ( u c (c ) λ u c (c ) ) b u cc (c )u c (c ) φ,j I E j=,2 u c (c = ( ) u c (c ) φ [ u c (c ) ) (b,2 b 2,) u ] cc(c ))u c (c ) = E u (c ) }{{}}{{} Ψ 3 Ψ 2 (2) [ [ β 2 u c (c 2, l2) ξ 2 λ 2s c (c 2, l2) λ 2 u c (c 2) u cc(c 2)s(c 2, l2) + φ 2 + u ]] cc(c 2) u c (c 2) (g + c 2 + l2 ) [ +I = κ 2 u (c )u cc (c 2) + κ u (c )u cc (c 2) ] [ I =2 κ 2 (3) u (c )u cc (c 2) + κ u (c )u cc (c 2) ] [ ] λ ( u c (c ) λ u c (c ) ) b,j u c (c u cc (c 2) φ ) I (E u (c }{{ = ( 2)) u } (c ) φ [ ] u (c ) ) ( b,2 b 2 u (c ),) (Evu (c 2)) u cc(c 2) }{{} Ψ 4 Ψ 5

11 where I x s an ndcator functon equal to one f x holds. Moreover, we have that: (4) (5) λ = Eλ u c (c ) E u c (c ) = E λ u c (c ) u c (c 2) E u c (c 2) u c (c ) u c (c φ = E φ ) Eu c (c ) = E u c (c ) u c (c 2) φ 2 E u c (c 2) u c (c ) and and λ u c (c ) = λ 2 u c (c 2) φ u c (c ) = φ 2 u c (c 2) (), (2) and (3) represent the FOCs wth respect to c, c and c 2 respectvely. (4) and (5) defne the (stochastc) propertes of the multplers and derve from the frst order condtons wth respect to the bonds. There are several noteworthy features: Frst, note that as (4) and (5) show, the ratos λ t u c(c t ) φ and t follow a (rsk adjusted) random walk process. Followng the argument of AMSS 9 u c(c when t ) markets are ncomplete, government debt and taxes become more persstent snce these multplers are state varables. In contrast, under a complete fnancal market, the multplers reman constant, the state vector n ths case, ncludes only the spendng levels and the ntal debt b. Second, the hghlghted terms Ψ to Ψ 5 are mportant for the optmal tax polcy under both complete and ncomplete markets. These terms reveal the ncentves of the planner to twst nterest rates n order to reduce the real payout of government debt (e.g. Char and Kehoe (999), Lustg et al (28) and FMOS (25 b)). Consder (for example) the term Ψ n (). When b >, the government wants to reduce the margnal utlty u c (c ), ths accomplshes to lower the nterest rate whch s pad at t = to rollover ths debt. Lowerng u c (c ) requres to lower taxes n t =. Smlarly, Ψ 2 to Ψ 5 relate to debt ssued n t = and capture changes n the tax schedule whch alter real rates n t =, 2. Consder the case where g = g H ; Under ncomplete markets we wll have λ u c(c ) > λ u c(c ) (see AMSS); the margnal utlty n t = decreases to lower the debt burden f j b,j >. The same apples to the term Ψ 4. Ψ 3 and Ψ 5 present an open economy verson of nterest rate twstng, they relate to the movements n th multpler φ t. Followng the prevous λ dscusson, when markets are complete we have that t = λ t+ and φ t = φ t+ u c(c t ) u c(c t+ ) u c(c t ) u c(c t+ ). Hence, Ψ 2 =... = Ψ 5 =. 3 Optmal Polcy 3. Fscal Unons In the closed economy, the role of debt management s to smooth tax dstortons over tme. the open economy, however, tax smoothng does not pertan only to wardng off ntertermporal tax dstortons, but also to smoothng dstortons stemmng from taxes and consumpton devatng across countres. A useful benchmark to whch we wll compare our results s the fscal unon, whereby the planner can use lump sum transfers and countres ssue debt commonly. Let T t be the transfer receved by the government n country n t and T t the analogous transfer to country 2 (so that net transfers equal zero). When transfers are allowed we can wrte the 9 AMSS work wth a Lagrangan where the multpler on the budget constrant s λ t = λ t u c(c t ), they multply the government budget constrant wth the margnal utlty of consumpton. In

12 government budget constrants n t = as b + b = b + g τ ( l ) + T and b 2 + b 2 = b 2 + g τ 2 ( l 2 ) T whch can be merged nto: b + b = b + g τ ( l ).e. n a sngle budget constrant where the spendng of both countres can be ether fnanced through common bonds. Now the two governments ssue bonds together, t s only the consoldated constrant whch matters for allocatons. Defne the jont debt as b b and b b. Analogously, defne total government debt ssued n perod as b b. The Ramsey program n ths economy can be represented as: Program 2 max E subject to b = b u c (c 2) u c (c ) u c (c ) βe u c (c 2) + b u c (c ) ) βe u c (c (c t + gt + lt ) = =,2 In the appendx we prove the followng: Lemma. t=,,2 β t u(c t, lt) =,2 b + b = [b s(c, l)] =,2 s(c, l ) = b u c (c ) βu c (c 2) s(c 2, l 2) u c (c ) E u c (c t) = u c(c j ) Eu c (c j t),, j =, 2 j, t =, 2 and u c (c 2) u c (c ) = u c(c j 2) u c (c j ) Equlbra wth fscal transfers. Consder the economy of secton 2, however, allow for transfers to be made across countres. Let b b + b 2. We can show that taxes satsfy: τ t = τ(g t + g 2 t, b ), t =, 2, τ t = τ 2 t for t =,, 2. When g are perfectly negatvely correlated, t holds that τ = τ 2 = τ and τ = τ τ (wth equalty f b = ). In ths case governments ssue only one bond, whether short or long becomes mmateral. and short term savngs. When g are perfectly postvely correlated, governments ssue a portfolo of long debt For the sake of brevty we derve the proof of Lemma n the appendx. There are however several ponts worth clarfyng: Frst, note that both n the case of dosyncratc and aggregate shocks we have that taxes are functons of aggregate spendng and overall ntal debt. The ntertermporal propertes of taxes therefore resemble the propertes of taxes n the closed economy and under a complete fnancal market. Ths should not be surprsng: If we assume that g = 2g then snce shocks are purely dosyncratc fscal transfers can eradcate all of the rsk related to government spendng. Practcally, ths means that we can omt all expectaton operators from Program 2, the soluton wll smply be a polcy rule (c t, l t), for t =,, 2 ndependent of the shock realzatons. Because the shocks become rrelevant, one maturty s suffcent to smooth taxes ntertemporally, t should not be surprsng that to complete the market, the planner can set (for example) b = and roll over the ntal lablty b usng short debt. Now consder the case of aggregate shocks. We have that g {2g L, 2g H }. Notce that f t 2

13 holds that c t = c 2 t and lt = lt 2, then Program 2 becomes equvalent to an optmal polcy program n the closed economy; The results of ABN hold and t s optmal to ssue short term savngs and long term debt. These propertes are further dscussed n the appendx. A fnal comment ends ths subsecton. Note that the equlbrum wth fscal transfers, can concde wth the decentralzed compettve equlbrum wth state contngent debt f and only f we have that b = b 2. In other words, f the ntal debt levels of the two countres are equal to one another. Fscal transfers can redstrbute the ntal debt across countres, all that matters for the allocaton s the sum b. In a decentralzed setup ths allocaton can be approxmated f debt redstrbuton s not necessary. In the followng sectons we wll mantan the assumpton b = b 2, ths wll enable us to compare the decentralzed equlbra we wll study wth the fscal unon outcome. 3.2 Debt Management under Idosyncratc Shocks We now resume the analyss of the optmal polcy problem wthout fscal transfers. Notce that n contrast to the fscal unon outcome whch features c t = c 2 t for all t, n our model where governments do not ssue debt commonly we have that uc(c 2 ) = uc(c2 u c(c 2 ) ) u c(c 2 ). In other words, t s the growth rate of margnal utlty whch s equal across countres, and not the levels of margnal utlty. Our am s to nvestgate to what extent the planner can target, through debt management, an allocaton where the dfferences n margnal utlty across countres are small even though they may be permanent. Put dfferently, we want to see whether the polcy can approxmate the fscal unon-complete market outcome descrbed prevously. We begn by showng that the optmal allocaton whch solves Program can be derved through a subset of the debt nstruments assumed. The followng proposton explans that we can elmnate foregn debt from one of the government budget constrants (ether n country or n country 2). Proposton. The optmal allocaton whch solves Program s equvalent to an allocaton whch maxmzes utlty subject to the constrant set and sets b, = b, = b, = ether for = or for = 2. Proof. Assume wthout loss of generalty that we set b 2, = b 2, = b 2, = so that all of government debt n country 2 becomes domestc. Let the allocaton (c, t, l, t ) be a soluton to the maxmzaton Program and (b 2,,, b 2,,, b 2,,) (,, ). Let us defne a new vector B, the elements of ths vector are the bonds, and let (b 2,, b 2,, b 2,) = (,, ). From (7), (9) and () we can set b,2 = b,,2 b 2,,, b,2 = b,,2 b 2,, and b,2 = budget constrants n every perod we need to set b 2,2 = and b, =, b, + b,,2 b,2, b t, = b, t, + b,, 2, b,2 b,. Moreover, to satsfy the government b 2,,2 + unaffected, the constrant set n the planner s program does not change. (c, t the new constrant set. b 2,,, b 2 t,2 = b 2, t,2 + b 2, t,, for t =, t,2 b t,2. Snce under the new portfolos bond prces are, l, t ) s feasble under Consder now the soluton to the planner s Program when we mpose as constrants b 2, = b2, = b 2, =. For clarty, denote the constraned problem by P 3. Suppose that the soluton to P 3 s (ĉ t, ˆl t). Snce n Program the planner can always set b 2, = b 2, = b 2, = t must be that t=,,2 βt u(c, t, l, t ) t=,,2 βt u(ĉ t, ˆl t). Moreover, snce (c, t, l, t ) s feasble under P 3 t must be that (ĉ t, ˆl t) = (c, t, l, t ). 3

14 Ths result s not surprsng. Snce both postve and negatve bond postons are admssble for every maturty we need three types of debt (nstead of four) to obtan the optmal allocaton. two bonds whch enable governments to trade domestcally and another bond whch allows for ntercountry trades. Clearly, t s nconsequental exactly whch country ssues the foregn debt. The result clearly hnges on the equalty of returns across countres n equlbrum. Snce both foregn and domestc debt of a gven maturty offer the same return (state by state and perod by perod) there s no reason why the households should prefer to hold foregn over domestc bonds Portfolos gven allocatons We now proceed to characterze the optmal portfolos whch solve Program. We begn by lookng at whether ths program admts a soluton for the portfolos when we apply the analyss of ABN. To do so we frst assume that the soluton to Program represents a complete market allocaton. Let (c, t, l, t ) be ths soluton to Program and further assume that b 2, 2,, = b, = b 2,, = (Proposton ). Proposton 2 n Angeletos (22) tells us that f the planner can ssue debt n maturtes wth ndependent returns then she can approxmate arbtrarly well the optmal allocaton n an economy wth state contngent (Arrow-Debreu) securtes. When ths allocaton can be approxmated through short and long bonds we can determne the optmal portfolos as follows: Frst, from (9) and () we derve the ntertemporal constrants: βu c (c, 2 ) u c (c, [( l, 2 ) g c, 2 ] + ( l, ) g c, ) (6) = b, for g {g L, g H },2 u c (c, ) βe u c (c, ), u c (c + b, 2 ),2 u c (c, ) u c (c, ) βe u c (c, 2 ) Denote the LHS of (6) by z. Followng the argument n Buera and Ncoln (26), z s a random varable wth two possble realzatons {z L, z H } dependng on whether g = g L or g = g H. Analogously, let ω uc(c, 2 ) denote the (random) margnal utlty rato. We have that ω u c(c, ) {ω L, ω H }. The optmal mx between short and long bonds s a soluton to the followng system of equatons: (7) u c(c, ), u c(c βeu c(c, ) ) βeu c(c, u c(c, ), u c(c βeu c(c, ) ) βeu c(c, )ω L 2 } {{ 2 )ω H } A [ b,,2 b,,2 ] }{{} B = [ z L z H ] }{{} Z The above system has a unque soluton f rank(a) = 2. Ths s satsfed f and only f ω L ω H. Gven ths soluton (f t exsts) we can derve the optmal bond portfolo for domestc government debt. We have: where ɛ I = [ βu c (c, 2 ) u c (c, b,,2, 2 ) [( u l(l u c (c, )( l, 2 ) g] + ( u l(l, 2 u c (c, u c(c, ) βeu c(c, = b,,, + b ),2 u c (c, ) βeu c (c, ) u c(c, ) βeu c(c, ], u c(c2 ) 2 ) u c(c, ), u c (c + b, ), βeu c (c, 2 ) )( l, ) g ɛ u c (c, 2 ) u c (c, ). Usng matrx notaton we can obtan the soluton 4

15 , for b, and b,, through solvng the followng system: (8) ) [( u l(l, 2 u c(c, ), u c(c βeu c(c, ) ) βeu c(c, u c(c, ), u c(c βeu c(c, ) ) βeu c(c, )ω L 2 } {{ 2 )ω H } C 2 ) g] + ( u l(l, [ b,, b,, ] }{{} D = [ s L s H ] }{{} S where s βuc(c, 2 ) )( l, u c(c, u c(c, )( l, 2 u c(c, ) g ɛ s the present value of the government surplus mnus the present value of foregn debt when =. The soluton to (8) s unque, agan, f we have ω H ω L Symmetrc Equlbra The above systems provde the soluton for government portfolos gven an allocaton (c, t, l, t ). The soluton can be found provded that bond prces n every country are dfferent n hgh spendng states than they are when spendng s low, or, when the rato uc(c, 2 ) vares wth u c(c, ) g. Followng the argument n ABN, the government can then choose a portfolo whch delvers a captal gan n hgh spendng states, ths mtgates the need to rase revenue from dstortonary taxes n these states. We now provde an example where uc(c, 2 ) are constant n u c(c, ) g and the optmal portfolos cannot be recovered through a soluton to the above systems of equatons. We begn by characterzng the vector of state varables whch nfluences the optmal allocaton. Lemma 2- State Varables Consder the soluton to Program. Let ψ t denote the vector of state varables whch nfluence the optmal allocaton n ths program n t =, 2. Let ψ t and ψ t denote the two possble realzatons of the state vector n t. In the case of dosyncratc shocks we have ψ = {g H, g L, Λ, B } and ψ = {g L, g H, Λ, B } where Λ {λ, λ 2, φ } and B s the vector of the bonds chosen n t =. Smlarly, n t = 2 we have: ψ2 = {g, g, Λ, Λ, B, B } ψ 2 = {g, g, Λ, Λ, B, B }. Lemma 2 s a standard result of AMSS. Under ncomplete markets the vector of states ncludes the Lagrange multplers λ t, t =, (here also φ t ) and the bonds ssued n prevous perods. Based on ths result we defne the followng equlbrum concept: Defnton 2- Symmetrc Equlbrum. Consder the soluton to Program. Let ψ t { ψ t, ψt } denote the vector of state varables whch nfluence the optmal allocaton n ths program n t. A symmetrc equlbrum s an allocaton (c, t, l, t ) whch satsfes: x = x 2, x t ( ψ t ) = x 2 t ( ψt ) for x = (c, l). A couple of remarks are n order: Frst, note that the symmetrc equlbrum defned above arses naturally n our setup, gven the structure of shocks and the fact that ntal debt levels b are the same across countres. In ths case we can speculate that the soluton to Program wll have the characterstcs of a symmetrc equlbrum, namely when (g, g 2 ) = (g H, g L ) the consumpton and lesure of country (2) wll be equal to the consumpton and lesure n 2 () f (g, g 2 ) = (g L, g H ). Ths can be verfed from the frst order condtons of the planner s program, when we assume that the multplers are not constant over tme. 5

16 Ths property cannot be establshed analytcally, we subsequently use numercal smulatons of the model to show that t holds. Second, the symmetrc equlbrum s a convenent concept snce t enables us to utlze systems (7) and (8) to characterze the optmal portfolo. The followng Lemma gves a key result of our analyss. Lemma 3. Assume a symmetrc equlbrum and dosyncratc shocks. Then gven (c, t, l, t ) the optmal portfolo cannot be recovered as a soluton to systems (7) and (8). Proof. Ths property follows from Defnton 2 and from the fact that n a symmetrc equlbrum under dosyncratc shocks we have that c t ( ψ t ) = c 2 t ( ψt ) and c t ( ψt ) = c 2 t ( ψ t ) for t =, 2. More crucally, the equlbrum n the bond market requres that c = c2 c. Ths mples that c 2 c 2 ( ψ ) 2 c 2 ( ψ = 2 ) c 2 ( ψ ) c 2 2 ( ψ = c ( ψ ) 2 ). In other words, the columns of the A and c 2 ( ψ2 ) C matrces n (7) and (8) are lnearly dependent because ω H = ω L and the optmal portfolos are not unquely dentfed Portfolos determne allocatons... We have now seen that under dosyncratc shocks the planner cannot replcate the complete market (fscal unon) outcome. More generally, gven an allocaton whch solves Program, the portfolo whch backs ths allocaton s not defned n the symmetrc equlbrum when shocks are dosyncratc. However, the prevous argument s based on the pressumpton that the portfolo does not nfluence the optmal allocaton (c, t, l, t ). Had our model been one of complete fnancal markets ths would have been exactly rght, long and short bonds could never be recovered from the soluton to the planner s program. Ths holds (for example) n the case of the fscal unon defned prevously. In that (symmetrc) equlbrum we had that c t = c 2 t across all realzatons of the dosyncratc shocks and snce all uncertanty was removed through transfers, whether a government ssued long or short bonds was mmateral for the allocaton. Under Program and dosyncratc shocks, however, markets are ncomplete. Ths mples that even though the allocaton cannot pn down unquely the maturty structure of debt, the maturty of bonds wll mpact the allocaton. To see ths consder agan [ the terms Ψ 2 to Ψ 5 n equatons (2) and (3). Consder for example the term ( λ λ u c(c ) u c(c )) j=,2 b u cc(c )uc(c ),j Eu c(c ]. Under ncomplete ) markets, when g = g H we wll have ( λ λ u c(c ) u c(c )) >. Therefore, f the government n country ssues short debt ( j=,2 b,j > ), the term Ψ 2 wll pull down the margnal utlty of consumpton. In contrast, f j=,2 b,j < the margnal utlty wll ncrease (relatve to the case where bonds are zero) when spendng ncreases. These effects capture the nterest rate twstng channel of polcy (Lustg et al (28), FMOS (25 b)). As dscussed prevously, under a complete market, we always have that ( λ λ u c(c ) u c(c )) =. Hence, nterest rate twsts cannot nfluence the allocaton. But f markets are ncomplete, then we may stll be able to defne unquely the portfolo because of the nterest rate twstng channel. We wll later show that ths s the case for dosyncratc shocks. To reterate we have showed that the equlbrum under dosyncratc shocks, cannot be a complete market outcome, whereby debt management can explot varatons n bond returns to smooth taxes across tme and countres. In a second step (ths subsecton) we argued that debt management may stll nfluence the allocaton under the ncomplete market. 6

17 3.3 Debt Management under Aggregate Shocks We now explan the propertes of the optmal allocaton when government spendng shocks are perfectly correlated across countres. As dscussed prevously, the equlbrum n the bond market gves rse to a cross country restrcton whch sets the margnal utlty rato n country equal to the rato n country 2. When shocks are dosyncratc (n a symmetrc equlbrum) ths restrcton leads to no varaton n bond returns across states; markets are ncomplete. In the case of aggregate shocks we can preserve the noton that the equlbrum s symmetrc. However, the cross country restrcton s now a dfferent one: Snce ψ = (g H, g H, Λ, B ) and ψ = (g L, g L, Λ, B ) we have that c ( ψ ) c 2 ( ψ = c2 ( ψ ) 2 ) c 2 2 ( ψ c ( ψ ) = c2 ( ψ ). 2 ) c 2 ( ψ2 ) c 2 2 ( ψ2 ) Notce that the above condtons tell us that the consumpton growth rates need to be equal c across countres when both countres experence a postve shock to spendng (.e. ( ψ ) c 2 ( ψ = c2 ( ψ ) 2 ) c 2 2 ( ψ ) 2 ) and separately they need to be equal across countres when they experence negatve spendng shocks ( c ( ψ ) = c2 ( ψ ) c 2 ( ψ2 ) c 2 2 ( ψ2 ) ). However, there s no restrcton mposed on Program whch equates the growth rates across spendng states. In equlbrum, long bonds can become agan useful for fscal hedgng purposes, ther prce wll vary across states. As we wll later show, the results of ABN apply n ths setup; the soluton to Program under aggregate shocks s the complete market allocaton, ths means that we wll be able to drop the multplers from the lst of state varables, only the spendng levels wll exert an nfluence on the allocaton. Moreover, snce g t = g 2 t for all t the soluton to ths model wll gve us a symmetrc equlbrum wth the property c t = c 2 t and l t = l 2 t for every t. In other words, the soluton to Program wll be the fscal unon outcome. To hghlght these propertes we make the followng remark: Remark : Assume aggregate shocks. The soluton to Program approxmates arbtrarly well the equlbrum outcome under a fscal unon. 4 Numercal Analyss 4. Calbraton We brefly descrbe the choce of parameters and functonal forms: As n Marcet and Scott (29), FMOS (25 a, b) we choose a perod utlty of the form u(c, l) = logc + η l+γ). We set γ = 2 and (+γ) choose the value of η so that n the determnstc steady state where b =, lesure s 3% of the tme endowment. 2 We normalze the tme endowment to unty, therefore total hours equal.7, whch s the steady state GDP n both economes. Our calbraton of spendng shocks s as follows: Frst, the average level of spendng g equals 25% of steady state GDP. We let g = g + ν where ν s a shock whch may take two values { σ, σ} wth u c(c ) Eu c(c t ) = uc(c2 ) u c(c Eu c(c 2 t ) 2 ) When shocks are aggregate, n a symmetrc equlbrum the constrants wll be ) slack. Moreover, snce countres experence the same shock net debt s equal zero. The objectve of the planner s to maxmze the sum of two concave utlty functons subject to the sequence of budget constrants. It s not dffcult to demonstrate that ths program s equvalent to maxmzng the utlty of each country separately subject to a sngle ntertemporal budget constrant as n ABN. 2 In the numercal experments, when we consder cases where ntal debt s hgher than zero, η s kept constant. u c(c ) = uc(c2 2 ) u c(c 2 7

18 equal probablty. As n Marcet and Scott (29) we set σ =.44. Hgher of lower values of σ exert no nfluence on the qualtatve patterns we document below. 4.2 Idosyncratc Shocks We frst document the behavor of taxes, consumpton and lesure n the models. In Fgures and 2 we assume b =. The top panels n Fgure plot the response of consumpton (left) and lesure (rght) n three perods, when spendng ncreases n t = (sold lne) and when t decreases (dashed lne). Wthout loss of generalty we can assume that g = g H and g 2 = g L. From the top panel of fgure whch plots the case of dosyncratc shocks we see that n response to the shocks, consumpton drops permanently n country and rses n country 2. Lesure remans constant over tme. Snce τ t = η (l t ) γ u c(c, taxes ncrease permanently after the shock and drop n t ) country 2 (left panel, Fgure 2). As dscussed prevously, when the shocks ht, the planner s objectve s twofold: ) to smooth taxes across tme and ) to smooth taxes across countres. The planner pursues these objectves subject to the compettve equlbrum (cross-country) restrcton that uc(c 2 ) = uc(c2 u c(c 2 ) ) u c(c whch suggests 2 ) that the devatons n consumpton across countres must be permanent. Gven ths restrcton, the exact path of consumpton n each country s determned by the optmal polcy. The fact that consumpton growth needs to be equal across countres, does not pn down (c, c 2). We may have (for nstance) that c < c and c 2 = c (where c s the pre shock level of consumpton) f we have that c 2 < c and c 2 2 > c. In other words, we can observe that country s consumpton returns to the steady state n t = 2, f country 2s consumpton starts below the steady state n t = and ends above c, preservng the equalty of the returns. In ths case, country s optmal path becomes smlar to the closed economy complete market allocaton, country 2s would be opposte to that benchmark. However, snce the undershootng of consumpton n country 2 s a large devaton from the Ramsey outcome, t becomes very dstortonary. Ths also holds when consumpton n country overshoots so that country 2 s closer to complete markets. It s clear from the fgure that the planner resolves ths tenson through settng c = c 2 < c 2 = c 2 2 n other words, through makng consumpton a pure random walk. Notce that an alternatve way to adjust consumpton and hours s to have lesure drop n country and rse n county 2 so that the gap between c t and c 2 t s smaller. At the extreme verson of ths scenaro we would have c t = c 2 t, l < l, l 2 > l and l 2 = l. In other words, all of the spendng shock s absorbed by lesure. Ths plan s however, s suboptmal for two reasons: frst, because a drop n lesure n country mples a drop n tax rates whch makes the government surplus devate from ts target level; second, because n terms of utlty, households care more about smoothng lesure ntertemporally than they do about smoothng consumpton, snce γ >. Snce n the optmal allocaton hours do not shft at all n response to the shocks, spendng shocks are bascally an exogenous change of ncome n two endowment economes, the random walk property of consumpton s a standard predcton of optmal consumpton theory. How far away s ths allocaton from the complete market outcome? To show the dfferences we plot n th mddle panel of Fgure, the fscal unon outcome. As dscussed prevously, the fscal unon concdes wth the complete fnancal market, snce shocks here are dosyncratc, there s perfect rsk sharng and therefore consumpton remans constnant over tme. Ths s clearly shown 8